Occlusions complicate the process of identifying individuals using their 3D facial scans. We propose a 3D face recognition system that automatically removes occlusion artifacts and identifies the facial image using regional classifiers. Automatic localization of occluded areas is handled by using a generic face model. Restoration of missing information after occlusion removal is performed by the application of an improved version of Gappy Principal Component Analysis (GPCA), which we call partial Gappy PCA (pGPCA). After the removal of noisy data introduced by realistic occlusions, occlusion-free faces are represented by local regions. Local classifiers operating on these local regions are then fused to achieve occlusion-robust identification performance. Our experimental results obtained on realistically occluded facial images from the Bosphorus 3D face database illustrate that our occlusion compensation scheme drastically improves the recognition accuracy from 78.05% to 94.20%.